Introduction to linear and nonlinear programming

Preface 1. The approximation problem and existence of best approximations 2. The uniqueness of best approximations 3. Approximation operators and some approximating functions 4. Polynomial interpolation 5. Divided differences 6. The uniform convergence of polynomial approximations 7. The theory of minimax approximation 8. The exchange algorithm 9. The convergence of the exchange algorithm 10. Rational approximation by the exchange algorithm 11. Least squares approximation 12. Properties of orthogonal polynomials 13. Approximation of periodic functions 14. The theory of best L1 approximation 15. An example of L1 approximation and the discrete case 16. The order of convergence of polynomial approximations 17. The uniform boundedness theorem 18. Interpolation by piecewise polynomials 19. B-splines 20. Convergence properties of spline approximations 21. Knot positions and the calculation of spline approximations 22. The Peano kernel theorem 23. Natural and perfect splines 24. Optimal interpolation Appendices Index.

Approximation theory and methods, by M. J. D. Powell. Pp 339. £25 (hardcover), £8·50 (paperback). 1981. ISBN 0-521-22472-1/29514-9 (Cambridge University Press)

With the demanding system requirements for the fifth-generation (5G) wireless communications and the severe spectrum shortage at conventional cellular frequencies, multibeam antenna systems operating in the millimeter-wave frequency bands have attracted a lot of research interest and have been actively investigated. They represent the key antenna technology for supporting a high data transmission rate, an improved signal-to-interference-plus-noise ratio, an increased spectral and energy efficiency, and versatile beam shaping, thereby holding a great promise in serving as the critical infrastructure for enabling beamforming and massive multiple-input multiple-output (MIMO) that boost the 5G. This paper provides an overview of the existing multibeam antenna technologies which include the passive multibeam antennas (MBAs) based on quasi-optical components and beamforming circuits, multibeam phased-array antennas enabled by various phase-shifting methods, and digital MBAs with different system architectures. Specifically, their principles of operation, design, and implementation, as well as a number of illustrative application examples are reviewed. Finally, the suitability of these MBAs for the future 5G massive MIMO wireless systems as well as the associated challenges is discussed.

Multibeam Antenna Technologies for 5G Wireless Communications

The proliferation of wireless services is driving innovative phased array solutions that are able to provide better cost/performance tradeoffs. In this context, the use of irregular array architectures provides a viable solution. This paper reviews and highlights some of the most recent advances in this field, including clustered, thinned, sparse, and time-modulated arrays, and their proposed design methodologies.

Unconventional Phased Array Architectures and Design Methodologies—A Review

From the material presented here, it is clear that the theory underlying the SNF approach is complex and involved to implement. However, it is also very elegant and provides one with many measurement options and powerful capabilities. The numerical implementation of the theory can be efficiently deployed through the use of the fast Fourier transform (FFT) enabling transforms of even electrically large antennas to be accomplished in a matter of a few seconds on a modern powerful digital computer. With the advent of commercially available SNF test systems, the user can exploit these techniques, largely unimpeded by the burden of the theory or the implementation thereof. The material presented here highlighted some of the fundamental concepts and limitations the user needs to be aware of in order to use these test systems with confidence.

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Spherical near-field antenna measurements

This work presents the analysis of power transmission of a radiating field inside the human head for microwave imaging applications. For this purpose, a spherical layered model composed of dispersive biological tissues is investigated in the range of (0.5–4) GHz and is confronted to experimental verification.

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Stratified spherical model for microwave imaging of the brain: Analysis and experimental validation of transmitted power

This paper deals with radiation pattern reconfigurable antenna in millimetre wave range. The innovative antenna system is based on an inhomogeneous HMFE lens (Half Maxwell Fish Eye) fed by sources array. The number of fed sources and the lens allow to both control the radiation pattern and to achieve a good efficiency. The global antenna permits to have beam shaping capability without phase shifters. Directive and sectorial radiation patterns can be obtained for both on-axis and off-axis configurations.

Reconfigurable antenna in mm-waves based on stratified lens and sources array

This paper deals with radiation pattern reconfigurable antenna in millimetre wave range. An active printed antenna array is designed in 24 GHz band and feed an inhomogeneous lens (Half Maxwell Fish Eye) to obtain reconfigurable patterns and in particular sectorial and directive cases. In the first part, the authors describe a four patches multilayer active array which allows achieving radiation pattern control by associating a commutator to each element and by changing the fed patches number. In a second part, this array feed an inhomogeneous lens to shape radiation pattern.

Millimeter Wave Reconfigurable Antenna Based on Active Printed Array and Inhomogeneous Lens

Near-field shaping at microwave or millimeter wave frequencies is an emerging field of study, able to accelerate a variety of technologies. Applications from sensing to medical imaging will benefit from accurate near-field shaping methods. In this communication, the use of convex optimization to shape the near field of a flat radiating aperture is investigated. The proposed approach, that is known to provide optimal solutions, is compared to existing near-field shaping methods.

On the use of convex optimization for electromagnetic near-field shaping

The phaseless characterization of antennas enables to reduce the cost and to ease the measurement of radiating systems, especially at high frequencies. The complex near field is retrieved from the acquisition of the antenna radiated field magnitude only, thanks to appropriate phase retrieval algorithms. Thus, a two-scan approach combined to a Gerchberg–Saxton algorithm has proven to lead to accurate phase retrievals. However, instead of measuring the field on two spherical surfaces of different radii as conventionally performed, we propose to measure the magnitude of the field on a single sphere but for two antenna positions. This new strategy is easier to implement in a number of measurement setups. Numerical and experimental validations in a commercial, arch-based, measurement system are shown and discussed.

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Benjamin Fuchs

Papers

Stratified spherical model for microwave imaging of the brain: Analysis and experimental validation of transmitted power

Reconfigurable antenna in mm-waves based on stratified lens and sources array

Millimeter Wave Reconfigurable Antenna Based on Active Printed Array and Inhomogeneous Lens

On the use of convex optimization for electromagnetic near-field shaping

Spherical Phaseless Antenna Measurements Experimental Validation of a Two-Antenna-Positions Procedure